Pretty much as many as you can afford to bring along.
You'll just need to provide your own transportation, lodging, and food.
When we attended, we saw everything ranging from the sole new appointee there on their own; just a parent or two; an entire immediate family; and entire clans!.
After the appointee reports, the families move on to other activities for the remainder of the day until the oath is administered at the end of the day. You are free to roam around much of West Point. There are activities in Ike Hall staffed by parent clubs from around the country.
We went all over West Point, and only were told to stay away from the cadet areas. If you parked yourself outside Grant Hall, you got a chance to view the streams of cadets leaving Thayer on their way to the cadet area.
The only real restricted event was the briefing in Washington Hall; at Ike Hall tickets were issued to parents/guardians to show up for the briefing at a particular time. Not sure if attendance was limited to only a few family members.
I encourage you to join prospective-net which does have quite a bit of information for the incoming class. Also consider joining the West Point Parents Facebook group, where Deb Dalton from the West Point Public Affairs Office, posts a lot of useful "official" information.
For the Class of 2014, we parents have our own discussion group to address questions, share information, and most important, share photos from Beast and other events as our cadets continue their journey.
PM me if any parents would like info on starting their own Class of 2015 parents group.
